Spanish side Sevilla are understood to be in for the forward again, having marked him as a target in the past, while Turkey's Fenerbahce are also intent on signing the former Chelsea and Manchester City attacker.
Sturridge spent the second half of the season on loan at West Brom after scoring a pair of Premier League goals for the Reds. However, he only managed six appearances for the Baggies as the result of injury, with the side also failing to remain in the English top flight.
The Anfield side signed the forward from Chelsea in 2013 and he went on to have a stellar first season with the side, scoring 21 goals in 29 appearances alongside Luis Suarez. While undoubtedly a talented and prolific scorer when healthy, a myriad of injury problems have stunted the player's career at Liverpool and he has dropped down the pecking order under Jurgen Klopp.
While he will be returning to the Reds for pre-season training next month, he will be fully aware of his status among his colleagues and is unlikely to remain with the side until the beginning of next season.
Liverpool are said to be willing to listen to offers for the oft-injured Englishman, yet they aren't willing to let him go on the cheap.
Sevilla, who chased Sturridge in January, are believed to have reignited their interest, but they will have to deal with competition in the form of Fenerbahce should the reports be believed.